Concave Pyramids of Second Sort -The Occurrence, Types, Variations
Abstract
Correspondingly to the method of generating the Concave Cupolae of second sort, the Concave Pyramids of second sort have the similar logic of origination, and their counterpart in regular faced convex pyramids (tetrahedron, Johnson's solids J1 and J2). The difference is that instead of onefold series of equilateral triangles in the lateral surface of the solid, there appear twofold series, forming deltahedral lateral surface with a common point, while bases are also regular polygons. This time, instead of the bases from n=3 to n=5, there are the basis from n=6 to n=9. The same lateral surface’s net can be folded and creased in two different ways, which produces the two types of Concave Pyramids of second sort: with a major and with a minor solid height. Combining and joining so obtained solids by the correspondent bases, the concave (ortho) bipyramids of second sort emerge, which then may be elongated, gyroelongated, and conca-elongated, creating a distinctive family of diverse concave... polyhedral structures.
Source:
Proceedings. Vol. 2 / 4th International Scientific Conference on Geometry and Graphics moNGeometrija 2014, June 20th - 22nd, 2014 Vlasina, Serbia, 2014, 157-168Publisher:
- Faculty of Civil Engineering and Architecture ; Serbian Society for Geometry and Graphics SUGIG, Niš ; Beograd
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GraFarTY - CONF AU - Obradović, Marija AU - Mišić, Slobodan AU - Popkonstantinović, Branislav PY - 2014 UR - https://grafar.grf.bg.ac.rs/handle/123456789/1252 AB - Correspondingly to the method of generating the Concave Cupolae of second sort, the Concave Pyramids of second sort have the similar logic of origination, and their counterpart in regular faced convex pyramids (tetrahedron, Johnson's solids J1 and J2). The difference is that instead of onefold series of equilateral triangles in the lateral surface of the solid, there appear twofold series, forming deltahedral lateral surface with a common point, while bases are also regular polygons. This time, instead of the bases from n=3 to n=5, there are the basis from n=6 to n=9. The same lateral surface’s net can be folded and creased in two different ways, which produces the two types of Concave Pyramids of second sort: with a major and with a minor solid height. Combining and joining so obtained solids by the correspondent bases, the concave (ortho) bipyramids of second sort emerge, which then may be elongated, gyroelongated, and conca-elongated, creating a distinctive family of diverse concave polyhedral structures. PB - Faculty of Civil Engineering and Architecture ; Serbian Society for Geometry and Graphics SUGIG, Niš ; Beograd C3 - Proceedings. Vol. 2 / 4th International Scientific Conference on Geometry and Graphics moNGeometrija 2014, June 20th - 22nd, 2014 Vlasina, Serbia T1 - Concave Pyramids of Second Sort -The Occurrence, Types, Variations EP - 168 SP - 157 UR - https://hdl.handle.net/21.15107/rcub_grafar_1252 ER -
@conference{ author = "Obradović, Marija and Mišić, Slobodan and Popkonstantinović, Branislav", year = "2014", abstract = "Correspondingly to the method of generating the Concave Cupolae of second sort, the Concave Pyramids of second sort have the similar logic of origination, and their counterpart in regular faced convex pyramids (tetrahedron, Johnson's solids J1 and J2). The difference is that instead of onefold series of equilateral triangles in the lateral surface of the solid, there appear twofold series, forming deltahedral lateral surface with a common point, while bases are also regular polygons. This time, instead of the bases from n=3 to n=5, there are the basis from n=6 to n=9. The same lateral surface’s net can be folded and creased in two different ways, which produces the two types of Concave Pyramids of second sort: with a major and with a minor solid height. Combining and joining so obtained solids by the correspondent bases, the concave (ortho) bipyramids of second sort emerge, which then may be elongated, gyroelongated, and conca-elongated, creating a distinctive family of diverse concave polyhedral structures.", publisher = "Faculty of Civil Engineering and Architecture ; Serbian Society for Geometry and Graphics SUGIG, Niš ; Beograd", journal = "Proceedings. Vol. 2 / 4th International Scientific Conference on Geometry and Graphics moNGeometrija 2014, June 20th - 22nd, 2014 Vlasina, Serbia", title = "Concave Pyramids of Second Sort -The Occurrence, Types, Variations", pages = "168-157", url = "https://hdl.handle.net/21.15107/rcub_grafar_1252" }
Obradović, M., Mišić, S.,& Popkonstantinović, B.. (2014). Concave Pyramids of Second Sort -The Occurrence, Types, Variations. in Proceedings. Vol. 2 / 4th International Scientific Conference on Geometry and Graphics moNGeometrija 2014, June 20th - 22nd, 2014 Vlasina, Serbia Faculty of Civil Engineering and Architecture ; Serbian Society for Geometry and Graphics SUGIG, Niš ; Beograd., 157-168. https://hdl.handle.net/21.15107/rcub_grafar_1252
Obradović M, Mišić S, Popkonstantinović B. Concave Pyramids of Second Sort -The Occurrence, Types, Variations. in Proceedings. Vol. 2 / 4th International Scientific Conference on Geometry and Graphics moNGeometrija 2014, June 20th - 22nd, 2014 Vlasina, Serbia. 2014;:157-168. https://hdl.handle.net/21.15107/rcub_grafar_1252 .
Obradović, Marija, Mišić, Slobodan, Popkonstantinović, Branislav, "Concave Pyramids of Second Sort -The Occurrence, Types, Variations" in Proceedings. Vol. 2 / 4th International Scientific Conference on Geometry and Graphics moNGeometrija 2014, June 20th - 22nd, 2014 Vlasina, Serbia (2014):157-168, https://hdl.handle.net/21.15107/rcub_grafar_1252 .